Unable to authenticate to SMTP server

I have installed the ISPconfig Virtual Appliance and have it running. I am using it primarily for e-mail. After much fooling around with my DNS records I have managed to receive e-mails using Thunderbird. I can connect to the POP3 server. I can send and receive e-mail using the web interface. I can send e-mails to others at my domain. However, I can't send e-mails to anyone else. When I try I get this error.

The specified server was found, but there was no response from the server.

I am hosting this on our library's server. This is for the public library where I work. We have a Wathcgaurd 500 firewall and I have enabled the SMTP rule which is port 25. This rule is however a port proxy (do you think that could be the problem?)

Here is some more information. I had a bad MX record in my DNS. Now things look better. I can now send and recieve from inside the Main Library building using an e-mail client such as Outlook (on the same network as the ISPConfig server)
From Outside the building I can recieve e-mails, and I can send to e-mails with the cass.lib.mi.us domain. I still cannot send to anyone other than cass.lib.mi.us e-mail accounts from outside the Main Library.

I suspect that this is some sort of relay setting problem. Can anyone advise me where I can check the relay settings, and what they should be set for in order for me to be able to send to non cass e-mails?

From Outside the building I can recieve e-mails, and I can send to e-mails with the cass.lib.mi.us domain. I still cannot send to anyone other than cass.lib.mi.us e-mail accounts from outside the Main Library.

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Is that the domain that is handled by your server? Then you should enable "Server requires authentication." in your email client. If you don't, and your server uses SMTP-AUTH, you can send only to domains that are on the server, not to external domains.